/lit/ - Literature

>>15074338
1,000,000 doors. You pick one. Then the host reveals all but one door to be goats. The obvious choice is to switch

switch, everyone knows that

Of course it does. This is as boring as a thread about whether 0.999... equals 1. Just go learn the math. Beliefs based on nothing but intuition are only interesting when no answer is known.

You can simulate this in a computer in two minutes and convince yourself.

It doesn't matter. It will be 50/50. I know everyone says >>15074376 but I personally can't make sense of their "proof" when intuitively, to me, it's just 50/50.

>>15074429
you’re being deceived by the process. You’re essentially betting on whether or not you picked the car. As long as there are 3+ doors, you should always switch, because your initial pick will have less than a 50% chance of being the car. In the 3-door case, it’s 1/3. So there’s a 2/3 chance that you picked the wrong door. So you should switch. See >>15074374
for intuitive answer

>>15074429
You're not gonna make it brah

>>15074429
The idea is that there is a 2/3’s chance of picking the first door wrong. After picking the first door, the host will never reveal the door with money but the door with the goat. So that 2/3’s odds of the other doors being right move to the singular unopened door that you didn’t pick

>>15074458
>>15074460

But there's only 2 doors and only one has the car so it's 50/50 even in this >>15074374 case.

>>15074528
no, there’s 3 doors. Your door has a 1/3 chance and the rest collectively have a 2/3 chance. Is the car behind your door or one of the other two? Which would you bet on?

>>15074560

But it turns into a choice between 2 doors

>>15074429
>intuitively
lmao
I bet excluded middle keeps you up at night

The "trick" to the question is that the host knows more than you do (he knows what's behind each door ahead of time), and he reveals some of that knowledge when he offers to switch.

>>15074338
I like goat very much sir
I take goat over car

>>15074429
idiot

>>15074581
what if the host offered you BOTH of the other doors? Surely you would pick those two over your initial pick? This shows that you believe the car is behind one of those two doors. And if that’s the case, then the host will eliminate all doors but the one with the car. Again, think about a case with 10 doors. Most likely, you first pick a goat, and the car is one of the other doors. The host will therefore make you choose between your door (1/10) chance and the other door (9/10) chance. I won’t make any more posts after this.

>>15074581
One of the doors is a random door that you picked.
One of the doors Monty looked at, said "I can't open the car door!" and didn't open.
Of course, maybe Monty is fucking with you. But there's only a 1/3 chance that he could be fucking with you, because that would require you to have already selected the door with the car!

Your intuition is tricking you because it wants Monty to choose a door randomly; more precisely, you probably always imagine him opening a particular door with a random thing behind it. But he can't do that without risking revealing the prize and spoiling the game.
However, there is a way to make Monty's choice random, satisfy your intuition, and preserve the game. If he chooses to open the door with the prize behind it, we simply swap the prize with the goat behind the unopened door.
The two unopened doors are identical, right? What do you care if we swap the prizes behind them?
When Monty intentionally only opens a door without the prize, he's doing the exact same thing in his head.

>>15074429
>>15074528
The door being opened by the host isn't random, they will ALWAYS open a wrong door, which means 2/3rd's of the time the host is leaving behind the right door. Don't think about the chances being rigged by the nature of picking between two doors, the chances are rigged because the host will NEVER open the right door.

>>15074429
Remember that the host isn’t opening a random door, they cannot open your door, or the door with the prize. If the host had to choose a random door, then you would be right.

>>15074338
>[Door1][Door2][Door3]
Your first choice has 2/3 chance of being a goat. That doesn't change.
Monty shows you that a different door has a goat and says "aye yo pal ya wanna finna switch?"
Now the odds you picked a goat are still 2/3 for that initial door. That never changed because you made the choice before the reveal. If you made the choice after then well of course you got a 50/50 shot. So we agree your choice was made during when you had a 2/3 shot of getting a goat.
If your initial door has a 2/3 shot of being a goat, then the door that hasn't been revealed has a 1/3 shot being the goat. Intuitively your mind should realize your initial choice had the highest chance of being a goat.
So if [choice][switch][goat revealed], then the choice door had a 2/3 chance of being a goat. Switch door has a 1/3 chance of being a goat. 3/3 - 1/3 gets you the chance of getting a car which is 2/3 for the switch door.

>>15074793
>The door being opened by the host isn't random, they will ALWAYS open a wrong door, which means 2/3rd's of the time the host is leaving behind the right door. Don't think about the chances being rigged by the nature of picking between two doors, the chances are rigged because the host will NEVER open the right door.

This is almost never explained in most problem statements though. Most of the time, people give the explanation as "Monty opens a door", without saying that he MUST open the door and that it couldn't be other than a goat. This is important, because you're on a gameshow, and the goal of a gameshow is to get sponsorship by keeping viewer's interest, so developing suspense through unpredictability is more important than sticking to a pointless formula.

Because of this, people are quite right to question the result and remain skeptical that switching necessarily gets you the 2/3 chance. "How am I supposed to know I'm no being tricked, how do I know the host isn't offering me to switch BECAUSE I have the car" your intuition says, and you intuition is right unless you have good reason to believe otherwise.

All explanations that rely on the idea that "you have 1/3 probability to choose right at the start, and this NEVER CHANGES" are just wrong, as they assume that probabilities aren't something that you revise as you gain further information. This logic only works if the host is guaranteed to always offer the switch to the goat, in which case being offered the switch gives you no further information about your initial choice and the logic works out.

It's notable that the original version of the Monty problem *didn't* have this stipulation, and rather let both the host and the contestant be free agents who could negotiate deals with each other, with the switch being an off the cuff request by the contestant trying to call Monty's bluff. It's really a more interesting take on the problem.

>>15075264
Scenario 1: You pick the car. Monty shows a goat. You switch to the other goat. You lose.

Scenario 2: You pick goat 1. Monty shows the other goat. You switch to the car. You win.

Scenario 3: You pick goat 2. Monty shows the other goat. You switch to the car. You win.

Scenario 4: You pick goat 1. Monty shows goat 2. You don’t switch. You lose.

Scenario 5: You pick goat 2. Monty shows you goat 1. You don’t switch. You lose.

Scenario 6: You pick the car. Monty shows you one of the goats. You don’t switch. You win.

It just shows probabilities are bs, as if third person would walk in after showing the empty door he has 50/50 change whichi is somehow different than the odds the contestant gets, when nothing objective has changed.

>>15074338
2 out of 3 times you picked a wrong door, the door with the goat opens, changing door will guarantee the win.

1 out of 3 times you picked the right door, the door with the goat opens, changing door will guarantee the loss.

Do you change your door ?

I thought the whole premise of this situation is that initially you have a 1 in 3 choice, but after getting it wrong you now have a 1 in 2 choice. The question to me is that do your odds increase because your offered to pick again ie switch? Initially the answer made sense to me, but the more I've thought about it, the less it does.

Why is switching considered a new 1 in 2 choice when weighing up your position and staying with your original choice not?

>>15075519
Yes, this is how it works when Monty can't choose anything and must show a goat.

If he's free to not do this, then he can do stuff like, only reveal a goat and offer the switch when you choose the car. This makes scenarios 2,3,4&5 instant losses, which aren't what's currently happening, and guarantees that you will always lose when you switch, since scenario 1 is the only thing that allows the problem statement to happen as stated, as everything else but that and scenario 6 is filered.

One you understand that Monty being given choice allows him to filter out your options, you should understand that he can affect the decision tree and deny branches to you, thus changing the possible probabilities.

Why doesn't somebody just fucking make a program that models this shitty problem and host it on a website and keep a tally so we can see which strat gives up more cars?
If you're so sure that it's one way or the other then let me see for myself with real data.
I've never seen anyone argue with real statistics, just hypotheses based on their own intuition.

>>15076838
write a program yourself, I've done it. Spoiler switching works half the time, not switching works one third of the time.

>>15074338
>people are unironically still arguing about this in the year 2020
You always switch, it’s obvious.
Just make a table of all of the possible outcomes and it becomes extremely apparent why this is the best option.
I fucking hate how these kinds of threads always out /lit/ posters as posturing brainlets.

Why the fuck is this thread so full of brainlets? It's really fucking simple, when you initially choose a door your chance of picking the reward is 1/3. That means there is a 2/3 chance for one of the other two remaining doors to have the car. When the host then opens a door with a goat, the remaining door has a 2/3 chance to have a car, while nothing changed about your initial 1/3 door. So of course you switch.

>>15076864
I'm not a soulless codemonkey.

>>15076838
>Why doesn't somebody just fucking make a program that models this shitty problem

Because programs will only model specific decision strategies that mush be locked in before the program runs. They cannot model the open problem of the host being freely able to choose what to do if that is left a possibility.

>>15076864
This is exactly what you'd expect to be the case given that the host chooses what door to reveal randomly.

The chances will be 2/3 to win if the host always reveals a goat you didn't pick.

The chances will be 0/3 if the host only reveals a goat if you picked the car.

>>15076873
>>15076878
It's not at all obvious and you only think it is because you've effectively memorized what you think of as being the solution without understanding why it works that way.

>>15076912
Not even slightly computer literate either basic google search for monty hall simulator
http://www.rossmanchance.com/applets/MontyHall/Monty04.html
http://www.shodor.org/interactivate/activities/SimpleMontyHall/
https://www.mathwarehouse.com/monty-hall-simulation-online/

All of them show to switch

>>15074338
this problem is a 105 iq brainlet filter

>>15076919
>It's not at all obvious
it's completely obvious when the situation isn't badly worded to bait people into getting the answer wrong.

For people wondering how picking a door first affects the decision between the two non-revealed doors: if there’s a goat behind your door (2/3 odds), then monty can’t reveal it. He has to reveal the other goat.

If you hadn’t picked a door at all, and monty still had to reveal one goat, he would have the choice between two goats to reveal, making it a 50/50 decision between the unrevealed doors.

But, in the probable event that you picked a goat door, you force monty to reveal the other goat, which tells you where the car is.

>>15076933
>when the situation isn't badly worded

Who's to judge that the situation is 'badly worded' though? Either the host is guaranteed to always offer the goat/switch in the problem or he is not. If this isn't stated, then the reader just has no reason to assume this, and so can't rely on assuming that Monty's actions aren't one off decisions. The original Monty Hall problem statement not only didn't actually make this guarantee, but made it clear that the decision to offer the switch was an action that was the result of negotiation/bartering between the host and the contestant. The idea that the host *must* always reveal a goat and offer the switch was a stipulation made later on in order to alter the problem into something more 'well defined'.

>>15074429
Unironically based for trusting your human spirit above the cold wheels of mathematics. Don't let these faggots take that from you

>>15075591
That's just because probabilities aren't inherent properties of things. They just express your partial information about things.

>>15076873
These threads are the same on /sci/

>>15076968
>Who's to judge that the situation is 'badly worded' though?
>The idea that the host *must* always reveal a goat and offer the switch was a stipulation made later on in order to alter the problem into something more 'well defined'
I mean you basically answered your question here, or at least substantiated what I said i.e. it's very common to explain this problem (and many other usual baiting /sci/ shitposts) ambiguously, since these posts exist almost solely to make people feel smart which is amplified when everybody else gets the answer wrong. There's a motive to be ambiguous. Once you realize that he always chooses a goat, and then take 5 seconds to think about what that means (2/3 of the time switching is correct, 1/3 it's not... wait... isn't it normally the other way around???) then it makes perfect sense. Once you have all the information to this problem it's totally trivial finding the answer. If intuitive means "simple to understand" then it's extremely intuitive. If it means "you can't use your faculties of reasoning to arrive at the answer" then nothing can be said to be actually intuitive. If it means "not immediately obvious" then sure, I agree with the sentiment that most people here are being smug about something that probably wasn't immediately obvious to them. But I reject the idea that thinking it's obvious means you don't understand why it works.

>>15076919
>>15077055
You're both faggots, it is in the hosts interest to win so he indeed MUST reveal a goat. if the host reveals the car you win immediately by picking it.

>>15074429
Imagine there are 1000 doors.
I open 998 of them and give you the option to switch them.
If you picked just two doors with no information, yeah it's fifty fifty chance. But you have information. Because if you stick with your door, you are basically saying that the odds the other door is right is the same as the door you picked out of 1000. So, is it just as likely that your 1 in 1000 pick is correct as when the person who cannot open the prize door closed all the other doors?

DESU that's the easiest, most practical way to understand this. If you can't, you're actually a retard and I'm sorry. You can admit you're wrong and I won't judge you but it isn't 50/50

holy fuck I have not seen /lit/ been triggered THIS hard for ages

>>15077217
The idea that increasing the number of doors makes any difference is something only complete brainlets can fathom. The only thing that matters is that the host is not opening doors randomly. So he is providing more information to you when he makes a selection. Hence you should switch.

>>15077055
>it's very common to explain this problem (and many other usual baiting /sci/ shitposts) ambiguously

Yes. And describing it ambiguously doesn't turn the problem into a non-problem, rather the ambiguous variations are far more rich and interesting precisely because they can't easily be reduced to a simple probability and can be analyzed with a greatly expanded set of methods. 'Solving' the problem where you observe what has happened, but have no guarantees on the host's behavior leads to a solution space that can factor in many things. There's nothing inherently wrong with posing the problem in its original form as long as you recognize it isn't equivalent to the fixed behavior version.

https://www.mdpi.com/2073-4336/8/3/31

>>15077082
>it is in the hosts interest to win

Says who? It's a gameshow, and the host will want to do whatever wins the show the best sponsors. Furthermore, him revealing a car would 'logically' result in you losing (given the host then has no reason to offer you the switch), which is still in his interest by your metrics.

>>15074338
2/3 to pick a goat in the first place. you get shown one goat, so the chance of you getting the valuable item remains 2/3 if you switch. why am i here

>>15076923
You only know the answer, and probably all the things in life, because you were told so.

>>15077471
Who says the contestant cant choose the open door with the car? Surely this would be the least interesting option for sponsors etc.
This do not extend this question in a meaningful way

>>15077497
I'd imagine there's some psychological reason to reject the idea that changing is better
Maybe its pride in the original choice, or incorrectly attempting to reduce the problem to a purely post reveal scenario

Switch to the revealed goat. 100% chance that you now have a cool goat.

The simplest way to understand this is to think about the question "should you switch?" as "Did you select a door with a goat behind it?" and this clearly shows that in 2/3 of cases you should switch.

People don't seem to understand that the fact a goat is revealed every time rather than a random door being revealed changes the whole dynamic of the riddle.

>>15074338
I never know how to solve this dilemma because I have more important matters at hand.
As an experienced wanker, I can only speak for myself, but I would not be surprised if the same can be said by other males.
I can spend at least an hour on the same jerk, prolonging the release of splooge. In doing so, a significant amount of love can preload in the shaft. Upon climax, all of the nectar releases at near maximum uncontrollable velocity and volume, being extremely satisfying until I realize I don't have enough toilet paper to cradle and contain the shame, for which the regret spills out on to my thighs and or the convulsions were so strong that some glue ended up on some perceptually important thing. This isn't a usual five to ten minute wank, like most males do. I'm sure it's similar to tantric sex. Having watched enough JAV, there is one series where I've seen this before where one male with a visibly flaccid penis (from prolonged pumping off-cam) ends up explosively venting all over a woman's face. This is very unlike most Western or European male actors that often have a piddly stream running out of their engorged third legs, despite having giant sacks, though they sometimes have empty bags as well. It's clear they don't fuck long enough and or they ejaculate so much during a shoot (off-cam, which I've seen in a documentary as a way of prolonging subsequent attempts at fucking without ejaculating due to being in a post-ejaculataion state where stimulation is 'harder' to do) that barely anything is left at the end for the money shot.

Is it normal that even if I understand that I should switch and it makes rational sense to me to do so - I understand the meaning behind it - it still seems weird?